Synopses & Reviews
The three-volume series
History of the Theory of Numbers is the work of the distinguished mathematician Leonard Eugene Dickson, who taught at the University of Chicago for four decades and is celebrated for his many contributions to number theory and group theory. This first volume in the series, which is suitable for upper-level undergraduates and graduate students, is devoted to the subjects of divisibility and primality. It can be read independently of the succeeding volumes, which explore diophantine analysis and quadratic and higher forms.
Within the twenty-chapter treatment are considerations of perfect, multiply perfect, and amicable numbers; formulas for the number and sum of divisors and problems of Fermat and Wallis; Farey series; periodic decimal fractions; primitive roots, exponents, indices, and binomial congruences; higher congruences; divisibility of factorials and multinomial coefficients; sum and number of divisors; theorems on divisibility, greatest common divisor, and least common multiple; criteria for divisibility by a given number; factor tables and lists of primes; methods of factoring; Fermat numbers; recurring series; the theory of prime numbers; inversion of functions; properties of the digits of numbers; and many other related topics. Indexes of authors cited and subjects appear at the end of the book.
Synopsis
This three-volume set, appropriate for upper-level undergraduate and graduate students, reviews the entire literature of number theory. Volume I focuses on material relating to divisibility and primality; Volume II, on the main landmarks of Diophantine analysis; and Volume III, on general theories rather than special problems and theorems. Accessible and well-indexed, the three books comprise the work of leading experts and can be used independently of each other.
Synopsis
This 1st volume in the series
History of the Theory of Numbers presents the material related to the subjects of divisibility and primality. This series is the work of a distinguished mathematician who taught at the University of Chicago for 4 decades and is celebrated for his many contributions to number theory and group theory. 1919 edition.
Synopsis
Written by a Univeristy of Chicago professor, this 1st volume in the 3-volume series History of the Theory of Numbers presents the material related to the subjects of divisibility and primality. 1919 edition.
Table of Contents
I. Perfect, multiply perfect, and amicable numbers
II. Formulas for the number and sum of divisors, problems of Fermat and Wallis
III. Fermats and Wilsons theorems, generalizations and converses; symmetric functions of 1, 2, ..., p-1, modulo p
IV Residue of (up-1-1)/p modulo p
V. Eulers function, generalizations; Farey series
VI. Periodic decimal fractions; periodic fractions; factors of 10n
VII. Primitive roots, exponents, indices, binomial congruences
VIII. Higher congruences
IX. Divisibility of factorials and multinomial coefficients
X. Sum and number of divisors
XI. Miscellaneous theorems on divisibility, greatest common divisor, least common multiple
XII. Criteria for divisibility by a given number
XIII. Factor tables, lists of primes
XIV. Methods of factoring
XV. Fermat numbers
XVI. Factors of an+bn
XVII. Recurring series; Lucas un, vn
XVIII. Theory of prime numbers
XIX. Inversion of functions; Möbius function; numerical integrals and derivatives
XX. Properties of the digits of numbers
Indexes